Assignment description:

This assignment will be worth 8% of the final grade.

You should write your code for each question  in a  .py file  (please  name  it  using the question name, e.g. q1.py). Please pack all your .py files into a single .zip file, name it using your student  ID  (e.g. if your student  ID  is  123456, then the file should  be  named as 123456.zip), and then submit the .zip file via Blackboard.

Please also write a text file, which provide the details about how to run your code for each question. The text file should be included in the .zip file as well.

Please  note that, the teaching assistant  may ask you to  explain the  meaning of your program, to ensure that the codes are indeed written by yourself. Please also note that we may  check whether your  program  is too  similar to your fellow  students’  code  using Blackboard.

This assignment is due on 5:00PM, 18 November (Friday). For each day of late submission, you will lose 10% of your mark in this assignment. If you submit more than three days later than the deadline, you will receive zero in this assignment.

Question 1 (10% of this assignment):

(Math: approximate the square root) There are several techniques for implementing the sqrt  function  in  the  math  module.  One  such  technique  is  known  as  the  Babylonian function. It approximates the square root of a number, n, by repeatedly performing a calculation using the following formula:

nextGuess = (lastGuess + (n / lastGuess)) / 2

When  nextGuess  and  lastGuess  are  almost  identical,  nextGuess  is  the  approximated square root. The initial guess can be any positive value (e.g., 1). This value will be the starting value for lastGuess. If the difference between nextGuess and lastGuess is less than a very small number, such as 0.0001, you can claim that nextGuess is the approximated square root of n. If not, nextGuess becomes lastGuess and the approximation process continues. Implement the following function that returns the square root of n.

def sqrt(n):

Question 2 (15% of this assignment):

(Emirp) An emirp (prime spelled backward) is a nonpalindromic prime number whose reversal is also a prime. For example, both 17 and 71 are prime numbers, so 17 and 71 are emirps. Write a program that displays the first 100 emirps. Display 10 numbers per line and align the numbers properly, as follows:

Question 3 (15% of this assignment):

(Financial: credit card number validation) Credit card numbers follow certain patterns: It must have between 13 and 16 digits, and the number must start with:

■ 4 for Visa cards

■ 5 for MasterCard credit cards

■ 37 for American Express cards

■ 6 for Discover cards

In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card numbers. The algorithm is useful to determine whether a card number is entered correctly or whether a  credit  card  is  scanned  correctly  by  a  scanner.  Credit  card  numbers  are  generated following this validity check, commonly known as the Luhn check or the Mod 10 check, which   can   be   described   as   follows   (for   illustration,   consider   the   card   number 4388576018402626):

1.   Double every second digit from  right to  left.  If doubling of a digit results  in a twodigit number, add up the two digits to get a single-digit number.

2.   Now add all single-digit numbers from Step 1.

4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37

3.   Add all digits in the odd places from right to left in the card number. 6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38

4.   Sum the results from Steps 2 and 3.

37 + 38 = 75

5.   If the result from Step 4 is divisible by 10, the card number is valid; otherwise, it is invalid. For example, the number 4388576018402626 is invalid, but the number

4388576018410707 is valid.

Write a program that prompts the user to enter a credit card number as an integer. Display whether the number is valid or invalid. Design your program to use the following functions:

Question 4 (15% of this assignment):

(Anagrams) Write a function that checks whether two words are anagrams. Two words are anagrams if they contain the same letters. For example, silent and listen are anagrams. The header of the function is:

def isAnagram(s1, s2):

(Hint: Obtain two lists for the two strings. Sort the lists and check if two lists are identical.)

Write a test program that prompts the user to enter two strings and, if they are anagrams, displays is an anagram; otherwise, it displays is not an anagram.

Question 5 (20% of this assignment):

(Game: locker puzzle) A school has 100 lockers and 100 students. All lockers are closed on the first day of school. As the students enter, the first student, denoted S1, opens every locker. Then the second student, S2, begins with the second locker, denoted L2, and closes every other locker. Student S3 begins with the third locker and changes every third locker (closes it if it was open, and opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker. Student S5 starts with L5 and changes every fifth locker, and so on, until student S100 changes L100.